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Diversity Within the Rijndael Design Principles for Resistance to Differential Power Analysis

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Book cover Cryptology and Network Security (CANS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10052))

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Abstract

The winner of the Advanced Encryption Standard (AES) competition, Rijndael, strongly resists mathematical cryptanalysis. However, side channel attacks such as differential power analysis and template attacks break many AES implementations.

We propose a cheap and effective countermeasure that exploits the diversity of algorithms consistent with Rijndael’s general design philosophy. The secrecy of the algorithm settings acts as a second key that the adversary must learn to mount popular side channel attacks. Furthermore, because they satisfy Rijndael’s security arguments, these algorithms resist cryptanalytic attacks.

Concretely, we design a 72-bit space of SubBytes variants and a 36-bit space of ShiftRows variants. We investigate the mathematical strength provided by these variants, generate them in SageMath, and study their impact on differential power analysis and template attacks against field-programmable gate arrays (FPGAs) by analyzing power traces from the DPA Contest v2 public dataset.

This work is sponsored by the Office of Naval Research under Air Force Contract FA8721-05-C-002. Opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by the United States Government.

M. Varia—Research performed while consulting at MIT Lincoln Laboratory.

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Notes

  1. 1.

    For instance, one can modify Manteena’s implementation of AES in VHDL [19, Appendix D] to produce different, static mappings of byte values in SubBytes, mappings of byte locations in ShiftRows, and matrix constants in MixColumns.

  2. 2.

    Our variants perform XOR, just as AES does. By contrast, Rijmen and Oswald [13] create variants that preserve AES’ original SubBytes functionality, at the cost of replacing XOR with a (slower and leakier) table lookup.

  3. 3.

    It is also possible to choose the primitive root of the polynomial used to represent elements of \({{\mathrm{GF}}}(256)\) [9]. This yields 3 bits of entropy independent of the affine transformation. However, SageMath encapsulates its choice of primitive root, so our work skips this extra flexibility.

  4. 4.

    We remark that Jing et al.’s calculation of this value [16] is inaccurate by a multiplicative factor of 7. Coincidentally, this 1/7 error closely matches the omitted 13.5 % throughput of SubBytes lacking fixed points.

  5. 5.

    This analysis generalizes to plaintext attacks.

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Acknowledgments

We gratefully acknowledge the support of Sukarno Mertoguno in the Office of Naval Research. The second author also acknowledges NSF grant 1414119. Additionally, we thank our colleagues Rob Cunningham and Ben Fuller for their valuable guidance and support.

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Authors and Affiliations

  1. MIT Lincoln Laboratory, Lexington, USA

    Merrielle Spain

  2. Boston University, Boston, USA

    Mayank Varia

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Correspondence to Merrielle Spain .

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  1. Università degli Studi di Milano, Crema, Italy

    Sara Foresti

  2. Università degli Studi di Salerno, Fisciano, Italy

    Giuseppe Persiano

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Spain, M., Varia, M. (2016). Diversity Within the Rijndael Design Principles for Resistance to Differential Power Analysis. In: Foresti, S., Persiano, G. (eds) Cryptology and Network Security. CANS 2016. Lecture Notes in Computer Science(), vol 10052. Springer, Cham. https://doi.org/10.1007/978-3-319-48965-0_5

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